R. Laskar

activity

20152019

collaborators

Showing math.COShow all

8 papers · 1 filter

math.CO2019

Properties of Partial Dominating Sets of Graphs

Benjamin M. Case, Todd Fenstermacher, Soumendra Ganguly +1

A set $S \subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$ . The domination number $γ (G)$ of $G$ equals the minimum cardina…

math.CO2019

$β$ -Packing Sets in Graphs

Benjamin M. Case, Evan M. Haithcock, Renu C. Laskar

A set $S \subseteq V$ is $α$ -dominating if for all $v \in V - S$ , $∣ N (v) \cap S ∣ \geq α ∣ N (v) ∣.$ The $α$ -domination number of $G$ equals the minimum cardinality of an $α$ -dominating se…

math.CO2018

Perfect Domination in Knights Graphs

Todd Fenstermacher, Soumendra Ganguly, Renu Laskar

For a graph $G = (V, E),$ a subset $S$ of $V$ is a perfect dominating set of $G$ if every vertex not in $S$ is adjacent to exactly one vertex in $S .$ The perfect domination number,…

math.CO2018

$P$ -Matchings in Graphs: A Brief Survey with Some Open Problems

Todd Fenstermacher, Soumendra Ganguly, Stephen Hedetniemi +1

For a graph $G = (V, E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed…

math.CO2017

Partial Domination in Graphs

Benjamin M. Case, Stephen T. Hedetniemi, Renu C. Laskar +1

A set $S \subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$ . The domination number $γ (G)$ of $G$ equals the minimum cardina…

math.CO2016

Split Domination, Independence, and Irredundance in Graphs

Stephen Hedetniemi, Fiona Knoll, Renu Laskar

In 1978, Kulli and Janakiram \citep{KulliJanakiramSplit} defined the split dominating set: a dominating set $S$ of vertices in a graph $G = (V, E)$ is called {\em split dominating}…